This is the documentation of the \texttt{MODULE Constants}, that
contains the definition of the most used mathematical
constants. This module uses numerical types defined in the
\texttt{MODULE NumTypes}.

\section{Name conventions}

All the real simple precision constants ends with \texttt{\_SP}, the
real double precision constants with \texttt{\_DP}, the complex simple
precision with \texttt{\_SPC} and the complex double precision with
\texttt{\_DPC}. 

If a there exist a real or complex constant of simple precison defined,
then it exist other with the same name (except for the sufix) of
double precision and viceversa.

\section{$\pi$-related constants}


\subsection{Real}

The complex $\pi$-related defined in this module and its values can be
seen in the table (\ref{tab:picteR})

\begin{table}[htbp]
  \centering
  \begin{tabular}{|l|l|c|}
    \hline
    \textbf{SP Name} & \textbf{DP Name} & \textbf{Value} \\
    \hline
    \hline
    \texttt{PI\_SP} & \texttt{PI\_DP} & $\pi$ \\
    \hline
    \texttt{TWOPI\_SP} & \texttt{TWOPI\_DP} & $2\pi$ \\
    \hline
    \texttt{HALFPI\_SP} & \texttt{HALFPI\_DP} & $\frac{\pi}{2}$ \\
    \hline
  \end{tabular}
  \caption{$\pi$-related real constants defined in the \texttt{MODULE constants}.}
  \label{tab:picteR}
\end{table}



\subsection{Complex}

The complex $\pi$-related defined in this module and its values can be
seen in the table (\ref{tab:picteC})

\begin{table}[htbp]
  \centering
  \begin{tabular}{|l|l|c|}
    \hline
    \textbf{SPC Name} & \textbf{DPC Name} & \textbf{Value} \\
    \hline
    \hline
    \texttt{UNITIMAG\_SPC} & \texttt{UNITIMAG\_DPC} & $\iota$ \\
    \hline
    \texttt{PI\_IMAG\_SPC} & \texttt{PI\_IMAG\_DPC} & $\pi\iota$ \\
    \hline
    \texttt{TWOPI\_IMAG\_SPC} & \texttt{TWOPI\_IMAG\_DPC} & $2\pi\iota$ \\
    \hline
    \texttt{HALFPI\_IMAG\_SPC} & \texttt{HALFPI\_IMAG\_SDC} & $\frac{\pi}{2}\iota$ \\
    \hline
  \end{tabular}
  \caption{$\pi$-related complex constants defined in the \texttt{MODULE constants}.}
  \label{tab:picteC}
\end{table}


\section{Square roots and $\log$ related constants}

We have only real constants defined here. We can see a list of
names-vlues in the table (\ref{tab:logcte})

\begin{table}[htbp]
  \centering
  \begin{tabular}{|l|l|c|}
    \hline
    \textbf{SP Name} & \textbf{DP Name} & \textbf{Value} \\
    \hline
    \hline
    \texttt{SR2\_SP} & \texttt{SR2\_DP} & $\sqrt{2}$ \\
    \hline
    \texttt{SR3\_SP} & \texttt{SR3\_DP} & $\sqrt{3}$ \\
    \hline
    \texttt{SRe\_SP} & \texttt{SRe\_DP} & $\sqrt{e}$ \\
    \hline
    \texttt{SRpi\_SP} & \texttt{SRpi\_DP} & $\sqrt{\pi}$ \\
    \hline
    \texttt{LG102\_SP} & \texttt{LG102\_DP} & $\log_{10}{2}$ \\
    \hline
    \texttt{LG103\_SP} & \texttt{LG103\_DP} & $\log_{10}{3}$ \\
    \hline
    \texttt{LG10e\_SP} & \texttt{LG10e\_DP} & $\log_{10}{e}$ \\
    \hline
    \texttt{LG10pi\_SP} & \texttt{LG10pi\_DP} & $\log_{10}{\pi}$ \\
    \hline
    \texttt{LGe2\_SP} & \texttt{LGe2\_DP} & $\log_e{2}$ \\
    \hline
    \texttt{LGe3\_SP} & \texttt{LGe3\_DP} & $\log_e{3}$ \\
    \hline
    \texttt{LGe10\_SP} & \texttt{LGe10\_DP} & $\log_e{10}$ \\
    \hline
  \end{tabular}
  \caption{Square roots and $\log$ related constants defined in the \texttt{MODULE constants}.}
  \label{tab:logcte}
\end{table}


\section{Other mathematical constants}

In this section we have only the Euler $\gamma$ constant. We can see
the name-value pair in the table (\ref{tab:other})

\begin{table}[htbp]
  \centering
  \begin{tabular}{|l|l|c|}
    \hline
    \textbf{SP Name} & \textbf{DP Name} & \textbf{Value} \\
    \hline
    \hline
    \texttt{GEULER\_SP} & \texttt{GEULER\_DP} & $\gamma (=0.5772\dots)$ \\
    \hline
  \end{tabular}
  \caption{Other mathematical constants defined in the \texttt{MODULE constants}.}
  \label{tab:other}
\end{table}
